Bastian Kubis

Cusps in K→3π decays

Abstract The pion mass difference generates a pronounced cusp in K → 3 π decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave ππ scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.

Towards a data-driven analysis of hadronic light-by-light scattering

The hadronic light-by-light contribution to the anomalous magnetic moment of the muon was recently analyzed in the framework of dispersion theory, providing a systematic formalism where all input quantities are expressed in terms of on-shell form factors and scattering amplitudes that are in principle accessible in experiment. We briefly review the main ideas behind this framework and discuss the various experimental ingredients needed for the evaluation of one- and two-pion intermediate states. In particular, we identify processes that in the absence of data for doubly-virtual pion–photon interactions can help constrain parameters in the dispersive reconstruction of the relevant input quantities, the pion transition form factor and the helicity partial waves for γ⁎γ⁎→ππ.

Precision calculation of the π−d scattering length and its impact on threshold πN scattering

We present a calculation of the pi^- d scattering length with an accuracy of a few percent using chiral perturbation theory. For the first time isospin-violating corrections are included consistently. Using data on pionic deuterium and pionic hydrogen atoms, we extract the isoscalar and isovector pion-nucleon scattering lengths and obtain a^+=(7.6 +/- 3.1) x 10^{-3} mpi^{-1} and a^-=(86.1 +/- 0.9) x 10^{-3} mpi^{-1}. Via the Goldberger-Miyazawa-Oehme sum rule, this leads to a charged-pion-nucleon coupling constant g_c^2/4 pi = 13.69 +/- 0.20.

High-Precision Determination of the Pion-Nucleon σ Term from Roy-Steiner Equations

We present a determination of the pion-nucleon (πN) σ term σ_{πN} based on the Cheng-Dashen low-energy theorem (LET), taking advantage of the recent high-precision data from pionic atoms to pin down the πN scattering lengths as well as of constraints from analyticity, unitarity, and crossing symmetry in the form of Roy-Steiner equations to perform the extrapolation to the Cheng-Dashen point in a reliable manner. With isospin-violating corrections included both in the scattering lengths and the LET, we obtain σ_{πN}=(59.1±1.9±3.0)  MeV=(59.1±3.5)  MeV, where the first error refers to uncertainties in the πN amplitude and the second to the LET. Consequences for the scalar nucleon couplings relevant for the direct detection of dark matter are discussed.

Precision calculation of threshold π−d scattering, πN scattering lengths, and the GMO sum rule

Abstract We use chiral perturbation theory (ChPT) to calculate the π − d scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) [1] , where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion–nucleon scattering lengths a + and a − . We study isospin-breaking contributions to the three-body part of a π − d due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a π − d due to virtual photons. Finally, we discuss the validity of the Goldberger–Miyazawa–Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion–nucleon coupling constant.

The

We calculate the omega --> pi0 gamma* and phi --> pi0 gamma* electromagnetic transition form factors based on dispersion theory, relying solely on a previous dispersive analysis of the corresponding three-pion decays and the pion vector form factor. We compare our findings to recent measurements of the omega --> pi0 mu+ mu- decay spectrum by the NA60 collaboration, and strongly encourage experimental investigation of the Okubo-Zweig-Iizuka-forbidden phi --> pi0 l+ l- decays in order to understand the strong deviations from vector-meson dominance found in these transition form factors.

\omega -> \pi^0 \gamma^*

We re-evaluate the electromagnetic corrections to η→3π decays at next-to-leading order in the chiral expansion, arguing that effects of order e2(mu−md) disregarded so far are not negligible compared to other contributions of order e2 times a light-quark mass. Despite the appearance of the Coulomb pole in η→π+π−π0 and cusps in η→3π0, the overall corrections remain small.

and

Abstract We analyze the CP-violating electric dipole form factor of the nucleon in the framework of covariant baryon chiral perturbation theory. We give a new upper bound on the vacuum angle, | θ 0 | ≲ 2.5 × 10 − 10 . The quark mass dependence of the electric dipole moment is discussed and compared to lattice QCD data. We also perform the matching between its representations in the three- and two-flavor theories.

\phi -> \pi^0 \gamma^*

The pion mass difference generates a pronounced cusp in K --> 3 pi decays, the strength of which is related to the pi pi S-wave scattering lengths. We apply an effective field theory framework developed earlier to evaluate the amplitudes for K_L --> 3 pi decays in a systematic manner, where the strictures imposed by analyticity and unitarity are respected automatically. The amplitudes for the decay eta --> 3 pi are also given.

transition form factors in dispersion theory

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the